The Colombia striker netted his 21st goal of the campaign in the 38th minute only to see his captain Gabi sent off for a second bookable offence on the stroke of halftime to leave Atletico with a man less for the entire second period.
Diego Simeone's side stood firm and moved on to 56 points from 25 games in second place, 12 behind leaders Barcelona, who came from behind to beat Sevilla 2-1 at home on Saturday.
Champions Real Madrid were third with 52 points after a 2-1 comeback win at basement side Deportivo Coruna, also on Saturday.
Simeone fielded a full strength side at the Calderon unlike other King's Cup semi-finalists Barca and Real, who meet for their second leg on Tuesday and Atletico's opponents Sevilla, who they visit on Wednesday.
Atletico put the visitors under intense pressure, eventually winning a penalty when the outstanding Diego Costa was brought down in the area.
Falcao sent the keeper the wrong way from the spot and with a man less following Gabi's sending off the hosts outwitted Espanyol in the second half to make it 13 league wins from 13 at the Calderon this season.
Javier Aguirre's visitors, 13th with 31 points, slipped to only their second defeat in 12 outings since the Mexican took the helm from Mauricio Pochettino with the side bottom in late November.
Earlier, Rayo Vallecano's push for European football next season suffered a blow when they lost 2-1 at home to Real Valladolid to stay seventh with 37 points.
Rayo defender Jordi Amat scored an own goal in the 71st minute but rectified the situation a minute later when he caught the visiting keeper off his line with a spectacular shot from around 40 metres out.
Former Manchester United striker Manucho grabbed the winner with ten minutes remaining to put Valladolid 11th on 33 points.
Elsewhere, new Celta Vigo coach Abel Resino started with a 2-1 home victory over former club Granada, as the Galicians notched a first win in seven outings.
Mario Bermejo's 81st-minute winner came from a wildly miss-hit shot which bounced inside the far post as the keeper watched helplessly. Celta stayed in the bottom three with 23 points.